The invention is based on a flow rate meter as defined hereinafter. A flow rate meter is already known (DE-OS 33 28 853), in which a flat substrate with a temperature-resistor layer applied onto it is retained in a flow of a medium by means of U-shaped retaining segments of retaining bodies. The electrically conductive retaining bodies are disposed extending parallel to one another, so that they are secured in a base body spaced widely apart from one another; as a result, not only is a large base body necessary, but the electrical connection to the retaining bodies are located far apart, which makes it more difficult to connect them electrically.